Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.

Access Full Article

Abstract

top
Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any p-i being integral multiples of 1 / m-i. A vector bundle V over Z equipped with an action of C is semistable (respectively, polystable) if and only if the parabolic bundle on X corresponding to V is semistable (respectively, polystable). This bijective correspondence is extended to the context of principal bundles.

@article{Biswas2003, abstract = {Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any p-i being integral multiples of 1 / m-i. A vector bundle V over Z equipped with an action of C is semistable (respectively, polystable) if and only if the parabolic bundle on X corresponding to V is semistable (respectively, polystable). This bijective correspondence is extended to the context of principal bundles.}, author = {Biswas, Indranil}, journal = {Collectanea Mathematica}, keywords = {Espacios y haces de fibras; Fibrados; Fibraciones principales; Superficies Riemann}, language = {eng}, number = {3}, pages = {293-308}, title = {Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.}, url = {http://eudml.org/doc/44320}, volume = {54}, year = {2003},}

TY - JOURAU - Biswas, IndranilTI - Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.JO - Collectanea MathematicaPY - 2003VL - 54IS - 3SP - 293EP - 308AB - Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any p-i being integral multiples of 1 / m-i. A vector bundle V over Z equipped with an action of C is semistable (respectively, polystable) if and only if the parabolic bundle on X corresponding to V is semistable (respectively, polystable). This bijective correspondence is extended to the context of principal bundles.LA - engKW - Espacios y haces de fibras; Fibrados; Fibraciones principales; Superficies RiemannUR - http://eudml.org/doc/44320ER -